58,889 research outputs found
Comparison of two non-primitive methods for path integral simulations: Higher-order corrections vs. an effective propagator approach
Two methods are compared that are used in path integral simulations. Both
methods aim to achieve faster convergence to the quantum limit than the
so-called primitive algorithm (PA). One method, originally proposed by
Takahashi and Imada, is based on a higher-order approximation (HOA) of the
quantum mechanical density operator. The other method is based upon an
effective propagator (EPr). This propagator is constructed such that it
produces correctly one and two-particle imaginary time correlation functions in
the limit of small densities even for finite Trotter numbers P. We discuss the
conceptual differences between both methods and compare the convergence rate of
both approaches. While the HOA method converges faster than the EPr approach,
EPr gives surprisingly good estimates of thermal quantities already for P = 1.
Despite a significant improvement with respect to PA, neither HOA nor EPr
overcomes the need to increase P linearly with inverse temperature. We also
derive the proper estimator for radial distribution functions for HOA based
path integral simulations.Comment: 17 pages, latex, 6 postscript figure
Principal manifolds and graphs in practice: from molecular biology to dynamical systems
We present several applications of non-linear data modeling, using principal
manifolds and principal graphs constructed using the metaphor of elasticity
(elastic principal graph approach). These approaches are generalizations of the
Kohonen's self-organizing maps, a class of artificial neural networks. On
several examples we show advantages of using non-linear objects for data
approximation in comparison to the linear ones. We propose four numerical
criteria for comparing linear and non-linear mappings of datasets into the
spaces of lower dimension. The examples are taken from comparative political
science, from analysis of high-throughput data in molecular biology, from
analysis of dynamical systems.Comment: 12 pages, 9 figure
A multidimensional grid-adaptive relativistic magnetofluid code
A robust second order, shock-capturing numerical scheme for multi-dimensional
special relativistic magnetohydrodynamics on computational domains with
adaptive mesh refinement is presented. The base solver is a total variation
diminishing Lax-Friedrichs scheme in a finite volume setting and is combined
with a diffusive approach for controlling magnetic monopole errors. The
consistency between the primitive and conservative variables is ensured at all
limited reconstructions and the spatial part of the four velocity is used as a
primitive variable. Demonstrative relativistic examples are shown to validate
the implementation. We recover known exact solutions to relativistic MHD
Riemann problems, and simulate the shock-dominated long term evolution of
Lorentz factor 7 vortical flows distorting magnetic island chains.Comment: accepted for publication in Computer Physics Communication
A sparse octree gravitational N-body code that runs entirely on the GPU processor
We present parallel algorithms for constructing and traversing sparse octrees
on graphics processing units (GPUs). The algorithms are based on parallel-scan
and sort methods. To test the performance and feasibility, we implemented them
in CUDA in the form of a gravitational tree-code which completely runs on the
GPU.(The code is publicly available at:
http://castle.strw.leidenuniv.nl/software.html) The tree construction and
traverse algorithms are portable to many-core devices which have support for
CUDA or OpenCL programming languages. The gravitational tree-code outperforms
tuned CPU code during the tree-construction and shows a performance improvement
of more than a factor 20 overall, resulting in a processing rate of more than
2.8 million particles per second.Comment: Accepted version. Published in Journal of Computational Physics. 35
pages, 12 figures, single colum
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